557 lines
26 KiB
C++
557 lines
26 KiB
C++
/*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public License
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* as published by the Free Software Foundation; either version 2
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* of the License, or (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*
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* The Original Code is Copyright (C) 2001-2002 by NaN Holding BV.
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* All rights reserved.
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*
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* The Original Code is: some of this file.
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*
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* */
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#ifndef __BLI_MATH_GEOM_H__
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#define __BLI_MATH_GEOM_H__
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/** \file
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* \ingroup bli
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "BLI_compiler_attrs.h"
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#include "BLI_math_inline.h"
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#ifdef BLI_MATH_GCC_WARN_PRAGMA
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# pragma GCC diagnostic push
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# pragma GCC diagnostic ignored "-Wredundant-decls"
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#endif
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/********************************** Polygons *********************************/
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float normal_tri_v3(float r[3], const float a[3], const float b[3], const float c[3]);
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float normal_quad_v3(float r[3], const float a[3], const float b[3], const float c[3], const float d[3]);
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float normal_poly_v3(float r[3], const float verts[][3], unsigned int nr);
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MINLINE float area_tri_v2(const float a[2], const float b[2], const float c[2]);
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MINLINE float area_squared_tri_v2(const float a[2], const float b[2], const float c[2]);
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MINLINE float area_tri_signed_v2(const float v1[2], const float v2[2], const float v3[2]);
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float area_tri_v3(const float a[3], const float b[3], const float c[3]);
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float area_squared_tri_v3(const float a[3], const float b[3], const float c[3]);
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float area_tri_signed_v3(const float v1[3], const float v2[3], const float v3[3], const float normal[3]);
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float area_quad_v3(const float a[3], const float b[3], const float c[3], const float d[3]);
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float area_squared_quad_v3(const float a[3], const float b[3], const float c[3], const float d[3]);
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float area_poly_v3(const float verts[][3], unsigned int nr);
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float area_poly_v2(const float verts[][2], unsigned int nr);
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float area_squared_poly_v3(const float verts[][3], unsigned int nr);
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float area_squared_poly_v2(const float verts[][2], unsigned int nr);
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float area_poly_signed_v2(const float verts[][2], unsigned int nr);
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float cotangent_tri_weight_v3(const float v1[3], const float v2[3], const float v3[3]);
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void cross_tri_v3(float n[3], const float v1[3], const float v2[3], const float v3[3]);
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MINLINE float cross_tri_v2(const float v1[2], const float v2[2], const float v3[2]);
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void cross_poly_v3(float n[3], const float verts[][3], unsigned int nr);
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float cross_poly_v2(const float verts[][2], unsigned int nr);
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/********************************* Planes **********************************/
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void plane_from_point_normal_v3(float r_plane[4], const float plane_co[3], const float plane_no[3]);
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void plane_to_point_vector_v3(const float plane[4], float r_plane_co[3], float r_plane_no[3]);
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void plane_to_point_vector_v3_normalized(const float plane[4], float r_plane_co[3], float r_plane_no[3]);
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MINLINE float plane_point_side_v3(const float plane[4], const float co[3]);
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/********************************* Volume **********************************/
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float volume_tetrahedron_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3]);
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float volume_tetrahedron_signed_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3]);
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bool is_quad_convex_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3]);
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bool is_quad_convex_v2(const float v1[2], const float v2[2], const float v3[2], const float v4[2]);
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bool is_poly_convex_v2(const float verts[][2], unsigned int nr);
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int is_quad_flip_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3]);
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bool is_quad_flip_v3_first_third_fast(const float v0[3], const float v1[3], const float v2[3], const float v3[3]);
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/********************************* Distance **********************************/
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float dist_squared_to_line_v2(const float p[2], const float l1[2], const float l2[2]);
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float dist_to_line_v2(const float p[2], const float l1[2], const float l2[2]);
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float dist_squared_to_line_segment_v2(const float p[2], const float l1[2], const float l2[2]);
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float dist_to_line_segment_v2(const float p[2], const float l1[2], const float l2[2]);
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float dist_signed_squared_to_plane_v3(const float p[3], const float plane[4]);
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float dist_squared_to_plane_v3(const float p[3], const float plane[4]);
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float dist_signed_to_plane_v3(const float p[3], const float plane[4]);
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float dist_to_plane_v3(const float p[3], const float plane[4]);
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/* plane3 versions */
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float dist_signed_squared_to_plane3_v3(const float p[3], const float plane[4]);
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float dist_squared_to_plane3_v3(const float p[3], const float plane[4]);
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float dist_signed_to_plane3_v3(const float p[3], const float plane[4]);
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float dist_to_plane3_v3(const float p[3], const float plane[4]);
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float dist_squared_to_line_segment_v3(const float p[3], const float l1[3], const float l2[3]);
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float dist_to_line_segment_v3(const float p[3], const float l1[3], const float l2[3]);
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float dist_squared_to_line_v3(const float p[3], const float l1[3], const float l2[3]);
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float dist_to_line_v3(const float p[3], const float l1[3], const float l2[3]);
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float dist_signed_squared_to_corner_v3v3v3(
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const float p[3],
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const float v1[3], const float v2[3], const float v3[3],
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const float axis_ref[3]);
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float dist_squared_to_ray_v3_normalized(
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const float ray_origin[3], const float ray_direction[3],
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const float co[3]);
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float dist_squared_ray_to_seg_v3(
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const float ray_origin[3], const float ray_direction[3],
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const float v0[3], const float v1[3],
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float r_point[3], float *r_depth);
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void aabb_get_near_far_from_plane(
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const float plane_no[3], const float bbmin[3], const float bbmax[3],
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float bb_near[3], float bb_afar[3]);
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struct DistRayAABB_Precalc {
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float ray_origin[3];
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float ray_direction[3];
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float ray_inv_dir[3];
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};
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void dist_squared_ray_to_aabb_v3_precalc(
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struct DistRayAABB_Precalc *neasrest_precalc,
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const float ray_origin[3], const float ray_direction[3]);
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float dist_squared_ray_to_aabb_v3(
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const struct DistRayAABB_Precalc *data,
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const float bb_min[3], const float bb_max[3],
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float r_point[3], float *r_depth);
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/* when there is no advantage to precalc. */
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float dist_squared_ray_to_aabb_v3_simple(
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const float ray_origin[3], const float ray_direction[3],
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const float bb_min[3], const float bb_max[3],
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float r_point[3], float *r_depth);
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struct DistProjectedAABBPrecalc {
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float ray_origin[3];
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float ray_direction[3];
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float ray_inv_dir[3];
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float pmat[4][4];
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float mval[2];
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};
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void dist_squared_to_projected_aabb_precalc(
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struct DistProjectedAABBPrecalc *precalc,
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const float projmat[4][4], const float winsize[2], const float mval[2]);
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float dist_squared_to_projected_aabb(
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struct DistProjectedAABBPrecalc *data,
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const float bbmin[3], const float bbmax[3],
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bool r_axis_closest[3]);
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float dist_squared_to_projected_aabb_simple(
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const float projmat[4][4], const float winsize[2], const float mval[2],
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const float bbmin[3], const float bbmax[3]);
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float closest_to_line_v2(float r_close[2], const float p[2], const float l1[2], const float l2[2]);
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float closest_to_line_v3(float r_close[3], const float p[3], const float l1[3], const float l2[3]);
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void closest_to_line_segment_v2(float r_close[2], const float p[2], const float l1[2], const float l2[2]);
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void closest_to_line_segment_v3(float r_close[3], const float p[3], const float l1[3], const float l2[3]);
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void closest_to_plane_normalized_v3(float r_close[3], const float plane[4], const float pt[3]);
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void closest_to_plane_v3(float r_close[3], const float plane[4], const float pt[3]);
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void closest_to_plane3_normalized_v3(float r_close[3], const float plane[3], const float pt[3]);
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void closest_to_plane3_v3(float r_close[3], const float plane[3], const float pt[3]);
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/* Set 'r' to the point in triangle (t1, t2, t3) closest to point 'p' */
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void closest_on_tri_to_point_v3(float r[3], const float p[3], const float t1[3], const float t2[3], const float t3[3]);
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float ray_point_factor_v3_ex(
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const float p[3], const float ray_origin[3], const float ray_direction[3],
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const float epsilon, const float fallback);
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float ray_point_factor_v3(
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const float p[3], const float ray_origin[3], const float ray_direction[3]);
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float line_point_factor_v3_ex(
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const float p[3], const float l1[3], const float l2[3],
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const float epsilon, const float fallback);
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float line_point_factor_v3(
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const float p[3], const float l1[3], const float l2[3]);
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float line_point_factor_v2_ex(
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const float p[2], const float l1[2], const float l2[2],
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const float epsilon, const float fallback);
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float line_point_factor_v2(
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const float p[2], const float l1[2], const float l2[2]);
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float line_plane_factor_v3(const float plane_co[3], const float plane_no[3],
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const float l1[3], const float l2[3]);
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void limit_dist_v3(float v1[3], float v2[3], const float dist);
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/******************************* Intersection ********************************/
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/* TODO int return value consistency */
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/* line-line */
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#define ISECT_LINE_LINE_COLINEAR -1
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#define ISECT_LINE_LINE_NONE 0
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#define ISECT_LINE_LINE_EXACT 1
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#define ISECT_LINE_LINE_CROSS 2
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int isect_seg_seg_v2(const float a1[2], const float a2[2], const float b1[2], const float b2[2]);
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void isect_seg_seg_v3(
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const float a0[3], const float a1[3],
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const float b0[3], const float b1[3],
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float r_a[3], float r_b[3]);
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int isect_seg_seg_v2_int(const int a1[2], const int a2[2], const int b1[2], const int b2[2]);
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int isect_seg_seg_v2_point_ex(
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const float v0[2], const float v1[2], const float v2[2], const float v3[2], const float endpoint_bias,
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float vi[2]);
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int isect_seg_seg_v2_point(
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const float v0[2], const float v1[2], const float v2[2], const float v3[2],
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float vi[2]);
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bool isect_seg_seg_v2_simple(
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const float v1[2], const float v2[2], const float v3[2], const float v4[2]);
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int isect_line_sphere_v3(const float l1[3], const float l2[3], const float sp[3], const float r, float r_p1[3], float r_p2[3]);
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int isect_line_sphere_v2(const float l1[2], const float l2[2], const float sp[2], const float r, float r_p1[2], float r_p2[2]);
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int isect_line_line_v2_point(
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const float v0[2], const float v1[2],
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const float v2[2], const float v3[2],
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float r_vi[2]);
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int isect_line_line_epsilon_v3(
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const float v1[3], const float v2[3],
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const float v3[3], const float v4[3],
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float i1[3], float i2[3],
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const float epsilon);
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int isect_line_line_v3(
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const float v1[3], const float v2[3],
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const float v3[3], const float v4[3],
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float r_i1[3], float r_i2[3]);
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bool isect_line_line_strict_v3(
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const float v1[3], const float v2[3],
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const float v3[3], const float v4[3],
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float vi[3], float *r_lambda);
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bool isect_ray_plane_v3(
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const float ray_origin[3], const float ray_direction[3],
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const float plane[4],
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float *r_lambda, const bool clip);
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bool isect_point_planes_v3(float (*planes)[4], int totplane, const float p[3]);
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bool isect_point_planes_v3_negated(
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const float (*planes)[4], const int totplane, const float p[3]);
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bool isect_line_plane_v3(
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float r_isect_co[3], const float l1[3], const float l2[3],
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const float plane_co[3], const float plane_no[3]) ATTR_WARN_UNUSED_RESULT;
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bool isect_plane_plane_plane_v3(
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const float plane_a[4], const float plane_b[4], const float plane_c[4],
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float r_isect_co[3]) ATTR_WARN_UNUSED_RESULT;
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bool isect_plane_plane_v3(
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const float plane_a[4], const float plane_b[4],
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float r_isect_co[3], float r_isect_no[3]) ATTR_WARN_UNUSED_RESULT;
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/* line/ray triangle */
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bool isect_line_segment_tri_v3(
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const float p1[3], const float p2[3],
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const float v0[3], const float v1[3], const float v2[3],
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float *r_lambda, float r_uv[2]);
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bool isect_line_segment_tri_epsilon_v3(
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const float p1[3], const float p2[3],
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const float v0[3], const float v1[3], const float v2[3],
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float *r_lambda, float r_uv[2], const float epsilon);
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bool isect_axial_line_segment_tri_v3(
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const int axis, const float p1[3], const float p2[3],
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const float v0[3], const float v1[3], const float v2[3], float *r_lambda);
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bool isect_ray_tri_v3(
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const float ray_origin[3], const float ray_direction[3],
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const float v0[3], const float v1[3], const float v2[3],
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float *r_lambda, float r_uv[2]);
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bool isect_ray_tri_threshold_v3(
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const float ray_origin[3], const float ray_direction[3],
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const float v0[3], const float v1[3], const float v2[3],
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float *r_lambda, float r_uv[2], const float threshold);
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bool isect_ray_tri_epsilon_v3(
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const float ray_origin[3], const float ray_direction[3],
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const float v0[3], const float v1[3], const float v2[3],
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float *r_lambda, float r_uv[2], const float epsilon);
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bool isect_tri_tri_epsilon_v3(
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const float t_a0[3], const float t_a1[3], const float t_a2[3],
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const float t_b0[3], const float t_b1[3], const float t_b2[3],
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float r_i1[3], float r_i2[3],
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const float epsilon);
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/* water-tight raycast (requires pre-calculation) */
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struct IsectRayPrecalc {
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/* Maximal dimension kz, and orthogonal dimensions. */
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int kx, ky, kz;
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/* Shear constants. */
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float sx, sy, sz;
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};
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void isect_ray_tri_watertight_v3_precalc(
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struct IsectRayPrecalc *isect_precalc, const float ray_direction[3]);
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bool isect_ray_tri_watertight_v3(
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const float ray_origin[3], const struct IsectRayPrecalc *isect_precalc,
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const float v0[3], const float v1[3], const float v2[3],
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float *r_dist, float r_uv[2]);
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/* slower version which calculates IsectRayPrecalc each time */
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bool isect_ray_tri_watertight_v3_simple(
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const float ray_origin[3], const float ray_direction[3],
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const float v0[3], const float v1[3], const float v2[3],
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float *r_lambda, float r_uv[2]);
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bool isect_ray_seg_v2(
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const float ray_origin[2], const float ray_direction[2],
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const float v0[2], const float v1[2],
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float *r_lambda, float *r_u);
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bool isect_ray_seg_v3(
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const float ray_origin[3], const float ray_direction[3],
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const float v0[3], const float v1[3],
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float *r_lambda);
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/* point in polygon */
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bool isect_point_poly_v2(const float pt[2], const float verts[][2], const unsigned int nr, const bool use_holes);
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bool isect_point_poly_v2_int(const int pt[2], const int verts[][2], const unsigned int nr, const bool use_holes);
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int isect_point_quad_v2(const float p[2], const float a[2], const float b[2], const float c[2], const float d[2]);
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int isect_point_tri_v2(const float pt[2], const float v1[2], const float v2[2], const float v3[2]);
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bool isect_point_tri_v2_cw(const float pt[2], const float v1[2], const float v2[2], const float v3[2]);
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int isect_point_tri_v2_int(const int x1, const int y1, const int x2, const int y2, const int a, const int b);
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bool isect_point_tri_prism_v3(const float p[3], const float v1[3], const float v2[3], const float v3[3]);
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bool isect_point_tri_v3(
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const float p[3], const float v1[3], const float v2[3], const float v3[3],
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float r_isect_co[3]);
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/* axis-aligned bounding box */
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bool isect_aabb_aabb_v3(const float min1[3], const float max1[3], const float min2[3], const float max2[3]);
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struct IsectRayAABB_Precalc {
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float ray_origin[3];
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float ray_inv_dir[3];
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int sign[3];
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};
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void isect_ray_aabb_v3_precalc(
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struct IsectRayAABB_Precalc *data,
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const float ray_origin[3], const float ray_direction[3]);
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bool isect_ray_aabb_v3(
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const struct IsectRayAABB_Precalc *data,
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const float bb_min[3], const float bb_max[3], float *tmin);
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bool isect_ray_aabb_v3_simple(
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const float orig[3], const float dir[3],
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const float bb_min[3], const float bb_max[3],
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float *tmin, float *tmax);
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/* other */
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#define ISECT_AABB_PLANE_BEHIND_ANY 0
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#define ISECT_AABB_PLANE_CROSS_ANY 1
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#define ISECT_AABB_PLANE_IN_FRONT_ALL 2
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int isect_aabb_planes_v3(
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const float (*planes)[4], const int totplane,
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const float bbmin[3], const float bbmax[3]);
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bool isect_sweeping_sphere_tri_v3(const float p1[3], const float p2[3], const float radius,
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const float v0[3], const float v1[3], const float v2[3], float *r_lambda, float ipoint[3]);
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bool clip_segment_v3_plane(
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const float p1[3], const float p2[3], const float plane[4],
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float r_p1[3], float r_p2[3]);
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bool clip_segment_v3_plane_n(
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const float p1[3], const float p2[3], const float plane_array[][4], const int plane_tot,
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float r_p1[3], float r_p2[3]);
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bool point_in_slice_seg(float p[3], float l1[3], float l2[3]);
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/****************************** Interpolation ********************************/
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void interp_weights_tri_v3(float w[3], const float a[3], const float b[3], const float c[3], const float p[3]);
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void interp_weights_quad_v3(float w[4], const float a[3], const float b[3], const float c[3], const float d[3], const float p[3]);
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void interp_weights_poly_v3(float w[], float v[][3], const int n, const float co[3]);
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void interp_weights_poly_v2(float w[], float v[][2], const int n, const float co[2]);
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void interp_cubic_v3(float x[3], float v[3],
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const float x1[3], const float v1[3], const float x2[3], const float v2[3], const float t);
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int interp_sparse_array(float *array, const int list_size, const float invalid);
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void transform_point_by_tri_v3(
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float pt_tar[3], float const pt_src[3],
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const float tri_tar_p1[3], const float tri_tar_p2[3], const float tri_tar_p3[3],
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const float tri_src_p1[3], const float tri_src_p2[3], const float tri_src_p3[3]);
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void transform_point_by_seg_v3(
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float p_dst[3], const float p_src[3],
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const float l_dst_p1[3], const float l_dst_p2[3],
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const float l_src_p1[3], const float l_src_p2[3]);
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void barycentric_weights_v2(
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const float v1[2], const float v2[2], const float v3[2],
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const float co[2], float w[3]);
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void barycentric_weights_v2_clamped(
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const float v1[2], const float v2[2], const float v3[2],
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const float co[2], float w[3]);
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void barycentric_weights_v2_persp(
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const float v1[4], const float v2[4], const float v3[4],
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const float co[2], float w[3]);
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void barycentric_weights_v2_quad(
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const float v1[2], const float v2[2], const float v3[2], const float v4[2],
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const float co[2], float w[4]);
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bool barycentric_coords_v2(const float v1[2], const float v2[2], const float v3[2], const float co[2], float w[3]);
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int barycentric_inside_triangle_v2(const float w[3]);
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void resolve_tri_uv_v2(float r_uv[2], const float st[2], const float st0[2], const float st1[2], const float st2[2]);
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void resolve_tri_uv_v3(float r_uv[2], const float st[3], const float st0[3], const float st1[3], const float st2[3]);
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void resolve_quad_uv_v2(float r_uv[2], const float st[2], const float st0[2], const float st1[2], const float st2[2], const float st3[2]);
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void resolve_quad_uv_v2_deriv(float r_uv[2], float r_deriv[2][2],
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const float st[2], const float st0[2], const float st1[2], const float st2[2], const float st3[2]);
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float resolve_quad_u_v2(const float st[2], const float st0[2], const float st1[2], const float st2[2], const float st3[2]);
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/* use to find the point of a UV on a face */
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void interp_bilinear_quad_v3(float data[4][3], float u, float v, float res[3]);
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void interp_barycentric_tri_v3(float data[3][3], float u, float v, float res[3]);
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/***************************** View & Projection *****************************/
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void lookat_m4(float mat[4][4], float vx, float vy,
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float vz, float px, float py, float pz, float twist);
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void polarview_m4(float mat[4][4], float dist, float azimuth,
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float incidence, float twist);
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void perspective_m4(float mat[4][4], const float left, const float right,
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const float bottom, const float top, const float nearClip, const float farClip);
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void orthographic_m4(float mat[4][4], const float left, const float right,
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const float bottom, const float top, const float nearClip, const float farClip);
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void window_translate_m4(float winmat[4][4], float perspmat[4][4],
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const float x, const float y);
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void planes_from_projmat(float mat[4][4], float left[4], float right[4], float top[4], float bottom[4],
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float front[4], float back[4]);
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void projmat_dimensions(const float projmat[4][4],
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float *r_left, float *r_right,
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float *r_bottom, float *r_top,
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float *r_near, float *r_far);
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int box_clip_bounds_m4(float boundbox[2][3],
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const float bounds[4], float winmat[4][4]);
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void box_minmax_bounds_m4(float min[3], float max[3],
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float boundbox[2][3], float mat[4][4]);
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/********************************** Mapping **********************************/
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void map_to_tube(float *r_u, float *r_v, const float x, const float y, const float z);
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void map_to_sphere(float *r_u, float *r_v, const float x, const float y, const float z);
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void map_to_plane_v2_v3v3(float r_co[2], const float co[3], const float no[3]);
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void map_to_plane_axis_angle_v2_v3v3fl(float r_co[2], const float co[3], const float axis[3], const float angle);
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/********************************** Normals **********************************/
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void accumulate_vertex_normals_tri_v3(
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float n1[3], float n2[3], float n3[3],
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const float f_no[3],
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const float co1[3], const float co2[3], const float co3[3]);
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void accumulate_vertex_normals_v3(
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float n1[3], float n2[3], float n3[3], float n4[3],
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const float f_no[3],
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const float co1[3], const float co2[3], const float co3[3], const float co4[3]);
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void accumulate_vertex_normals_poly_v3(
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float **vertnos, const float polyno[3],
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const float **vertcos, float vdiffs[][3], const int nverts);
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/********************************* Tangents **********************************/
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void tangent_from_uv_v3(
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const float uv1[2], const float uv2[2], const float uv3[2],
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const float co1[3], const float co2[3], const float co3[3],
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const float n[3],
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float r_tang[3]);
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/******************************** Vector Clouds ******************************/
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void vcloud_estimate_transform_v3(
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const int list_size, const float (*pos)[3], const float *weight, const float (*rpos)[3], const float *rweight,
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float lloc[3], float rloc[3], float lrot[3][3], float lscale[3][3]);
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/****************************** Spherical Harmonics *************************/
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/* Uses 2nd order SH => 9 coefficients, stored in this order:
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* 0 = (0, 0),
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* 1 = (1, -1), 2 = (1, 0), 3 = (1, 1),
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* 4 = (2, -2), 5 = (2, -1), 6 = (2, 0), 7 = (2, 1), 8 = (2, 2) */
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MINLINE void zero_sh(float r[9]);
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MINLINE void copy_sh_sh(float r[9], const float a[9]);
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MINLINE void mul_sh_fl(float r[9], const float f);
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MINLINE void add_sh_shsh(float r[9], const float a[9], const float b[9]);
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MINLINE float dot_shsh(const float a[9], const float b[9]);
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MINLINE float eval_shv3(float r[9], const float v[3]);
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MINLINE float diffuse_shv3(float r[9], const float v[3]);
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MINLINE void vec_fac_to_sh(float r[9], const float v[3], const float f);
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MINLINE void madd_sh_shfl(float r[9], const float sh[3], const float f);
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/********************************* Form Factor *******************************/
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float form_factor_quad(const float p[3], const float n[3],
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const float q0[3], const float q1[3], const float q2[3], const float q3[3]);
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bool form_factor_visible_quad(const float p[3], const float n[3],
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const float v0[3], const float v1[3], const float v2[3],
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float q0[3], float q1[3], float q2[3], float q3[3]);
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float form_factor_hemi_poly(float p[3], float n[3],
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float v1[3], float v2[3], float v3[3], float v4[3]);
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void axis_dominant_v3_to_m3_negate(float r_mat[3][3], const float normal[3]);
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void axis_dominant_v3_to_m3(float r_mat[3][3], const float normal[3]);
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MINLINE void axis_dominant_v3(int *r_axis_a, int *r_axis_b, const float axis[3]);
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MINLINE float axis_dominant_v3_max(int *r_axis_a, int *r_axis_b, const float axis[3]) ATTR_WARN_UNUSED_RESULT;
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MINLINE int axis_dominant_v3_single(const float vec[3]);
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MINLINE int axis_dominant_v3_ortho_single(const float vec[3]);
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MINLINE int max_axis_v3(const float vec[3]);
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MINLINE int min_axis_v3(const float vec[3]);
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MINLINE int poly_to_tri_count(const int poly_count, const int corner_count);
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MINLINE float shell_angle_to_dist(const float angle);
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MINLINE float shell_v3v3_normalized_to_dist(const float a[3], const float b[3]);
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MINLINE float shell_v2v2_normalized_to_dist(const float a[2], const float b[2]);
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MINLINE float shell_v3v3_mid_normalized_to_dist(const float a[3], const float b[3]);
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MINLINE float shell_v2v2_mid_normalized_to_dist(const float a[2], const float b[2]);
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/********************************* Cubic (Bezier) *******************************/
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float cubic_tangent_factor_circle_v3(const float tan_l[3], const float tan_r[3]);
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/**************************** Inline Definitions ******************************/
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#if BLI_MATH_DO_INLINE
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#include "intern/math_geom_inline.c"
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#endif
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#ifdef BLI_MATH_GCC_WARN_PRAGMA
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# pragma GCC diagnostic pop
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#endif
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#ifdef __cplusplus
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}
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#endif
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#endif /* __BLI_MATH_GEOM_H__ */
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